Boundedness of Solutions of a Quasi-periodic Sublinear Duffing Equation


Yaqun PENG,Xinli ZHANG,Daxiong PIAO.Boundedness of Solutions of a Quasi-periodic Sublinear Duffing Equation[J].Chinese Annals of Mathematics B,2021,42(1):85~104
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Yaqun PENG; Xinli ZHANG;Daxiong PIAO


This work was supported by the National Natural Science Foundation of China (Nos.,11571327, 11971059).
Abstract: The authors study the Lagrangian stability for the sublinear Duffing equations ddot{x}+e(t)|x|^{\alpha-1}x=p(t) with 0<\alpha<1,where e and p are real analytic quasi-periodic functions with frequency omega. It is proved that if the mean value of e is positive and the frequency omega satisfies Diophantine condition, then every solution of the equation is bounded.


Hamiltonian system, Sublinear Duffing equation, Boundedness, Quasiperiodic solution, Invariant curve


34C11, 34D20, 37E40, 37J40
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